I'm amused by the burying of the non-lede until half way through the paper. I, too, can maintain a 59-bit repetition code for over two hours on my quantum laptop (it's just a normal laptop, but it definitely obeys the laws of quantum mechanics):
Initialize the coded bit, using a 59-qubit repetition code that corrects bit flips but not phase errors, in IPython:
In [1]: A = 59 * (False,)
Write a decoder:
In [2]: def decode(physbits):
...: return sum(physbits) > len(physbits)/2.0
Wait two hours [0]. I'll be lazy and only decode at the end of the two hours, but if I wanted error correction to get the full advantage, I would periodically run the error correction algorithm and fix detected errors. Here's the decoding!
In [3]: decode(A)
Out[3]: False
Holy cow, it worked!
I'm being rather tongue-in-cheek here, of course. But it's genuinely impressive that my laptop can stick 59 bits into DRAM cells containing a handful of electrons each, and all of them are just fine after several hours. And it's really really impressive that this research group got their superconducting qubits to store classical states well enough that their rather fancy error correcting device could keep up and preserve the logical state for two hours. [1]
But this isn't quantum error correction going FOOM, per se. It's classical. A bit-flip-corrected but not phase-flip-corrected qubit is precisely a classical bit, no more, no less.
The authors did also demonstrate that they could do the same trick correcting phase flips and not bit flips, but that's a tiny bit like turning the experiment on its side and getting the same result. Combining both demonstrations is impressive, though -- regardless of whether you look at the DRAM cells in my laptop as though the level is the Z basis or the X basis, they only work in one single basis. You cannot swap the role of level and phase in DRAM and get it to still work. But the researchers did pull that off on their two-hour-half-life device, and I find that quite impressive, and the fact that it worked strongly suggests that their device is genuinely 59 qubits, whereas no one could credibly argue that my laptop contains giga-qubits of DRAM. Fundamentally, you can do classical repetition using a repetition code, but you cannot do quantum computation with it. You need fancier, and more sensitive-to-errors, codes for this, and that's what the second half of the article is about.
[0] I didn't actually wait two hours. But I could have waited a week and gotten the same result.
[1] The researchers' qubits are nowhere near as good as my DRAM. They had to run their error correction a billion times or so during the course of their two hours. (My DRAM refreshes quite a few times over the course of two hours, and one can look at DRAM refreshes as correcting something a bit like a repeptition code.)